Question

Three numbers form an arithmetic sequence whose

Answer 1

Let x be the first number in the sequence. Then the first three numbers are

{x, x + 3, x + 6}

The next sentence says that the sequence

{x + 1, x + 9, x + 25}

is geometric, which means there is some fixed number r for which

x + 9 = r (x + 1)

x + 25 = r (x + 9)

Solve for r :

r = (x + 9)/(x + 1) = (x + 25)/(x + 9)

Solve for x :

(x + 9)² = (x + 25) (x + 1)

x ² + 18x + 81 = x ² + 26x + 25

8x = 56

x = 7

Then the three numbers are

{7, 10, 13}